Exercise 6. Let (X, d) be a metric space. Given E C X, let E be...

 

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Exercise 6. Let (X, d) be a metric space. Given E C X, let Eº be the set of interior points of E. (The set E° is called the interior of E.) (a) If GCE is open, prove that G C Eº. (b) Prove that E° is an open set. (c) From the previous two parts, deduce that Eº is the union of all open subsets of E. Exercise 6. Let (X, d) be a metric space. Given E C X, let Eº be the set of interior points of E. (The set E° is called the interior of E.) (a) If GCE is open, prove that G C Eº. (b) Prove that E° is an open set. (c) From the previous two parts, deduce that Eº is the union of all open subsets of E.

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int E xcE x is an interion point of Ef Let point of E ... View the full answer